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Slow and Fast Decaying Solutions to a Critical Semilinear Parabolic Equation

Volume 4, Number 1 (2013), 1 - 10

Slow and Fast Decaying Solutions to a Critical Semilinear Parabolic Equation

Communicated By: 
Irena Lasiecka
Price: $20.00

Abstract

We study the decay rate to 0, as t −→ +∞ of the solution of equation ψt − Δψ − λ1ψ + |ψ|p−1ψ = 0 with homogeneous Dirichlet boundary conditions in a bounded smooth open connected domain of Rn where p > 1. We show that either ψ(t, ∙) converges to 0 faster than any negative power of t, or ψ(t, ∙) decreases like t− 1 p−1 .